Transformation of non positive semidefinite correlation matrices |
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Authors: | Peter J. Rousseeuw Geert Molenberghs |
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Affiliation: | Department of Mathematics and Computer Science , Universitaire Installing Antwerpen , Universiteitsplein 1, Wilrijk, B-2610, Belgium |
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Abstract: | In multivariate statistics, estimation of the covariance or correlation matrix is of crucial importance. Computational and other arguments often lead to the use of coordinate-dependent estimators, yielding matrices that are symmetric but not positive semidefinite. We briefly discuss existing methods, based on shrinking, for transforming such matrices into positive semidefinite matrices, A simple method based on eigenvalues is also considered. Taking into account the geometric structure of correlation matrices, a new method is proposed which uses techniques similar to those of multidimensional scaling. |
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Keywords: | eigenvalue method missing data multidimensional scaling multivariate probii model robust correlations shrinking |
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